Related papers: Asymptotic Fixed-Speed Reduced Dynamics for Kineti…
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
We explain how to find the asymptotic form of fixed point solutions in functional truncations, in particular $f(R)$ approximations. We find that quantum fluctuations do not decouple at large $R$, typically leading to elaborate asymptotic…
In particle systems, flocking refers to the phenomenon where particles' individual velocities eventually align. The Cucker-Smale model is a well-known mathematical framework that describes this behavior. Many continuous descriptions of the…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…
A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…
We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we…
In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe…
We consider the Navier--Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in…
This paper is devoted to the study of the asymptotic behaviors of the minimal speed of propagation of pulsating traveling fronts solving the Fisher-KPP reaction-advection-diffusion equation within either a large drift, a mixture of large…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…